Consider a small cylindrical tank with capped ends with an internal diameter (ID) of 25 mm and an outer diameter (OD) of 50 mm. The tank can be subjected to an outer pressure p0 and an inner pressure pi as shown in Figure 3-31 of your textbook. Your book calls the hoop stress σt and the radial stress σr. The equations for the hoop stress σθ, radial stress σr, and axial stress σz of the tank are given by:
σθ = (pi * (r^2 - R^2)) / (R^2 - r^2)
σr = (pi * (r^2 - R^2)) / (R^2 - r^2)
σz = (pi * (r^2 - R^2)) / (2 * (R^2 - r^2))
Note: your book calls the hoop stress σt and the radial stress σr. Use my terminology.
a. Using Matlab, plot the hoop, radial, and axial stresses of the thick-wall cylinder for the case pi = 150 MPa and po = 0. In addition, plot the hoop and axial stress for the thin-wall cylindrical pressure vessel solution. Plot all of these in the same figure. Put a legend on the figure, label the axes, and include units in your labels.
b. For the case in part a, compare the maximum normal stress and maximum shear stress for the thick-wall and thin-wall cylinders. How much larger or smaller (in terms of percentage) is the maximum normal stress and maximum shear stress for the thick-wall than the thin-wall model? Which model should be used to develop a conservative design for the tank? For this problem, turn in your Matlab code with your homework.
